Question

Calcúle a distância da reta P à reta r tendo o ponto P(1,3) e e a reta r: 3x+ 4y - 5=0

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm dist\hat ancia~do~ponto~\grave a~reta}\\\sf Dado~o~ponto~P(x_P,y_P)~e~uma~reta~\\\sf r: ax+by+c=0\\\sf a~dist\hat ancia~de~P~\grave a~r~\acute e~dada~por\\\sf D_{P,r}=\dfrac{|a\cdot x_P+b\cdot y_P+c|}{\sqrt{a^2+b^2}}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt dados\begin{cases}\sf P(1,3)\implies x_P=1~~y_P=3\\\sf r=3x+4y-5=0\implies a=3~~b=4~~c=-5\\\sf D_{P,r}=?\end{cases}\\\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf D_{P,r}=\dfrac{|a\cdot x_P+b\cdot y_P+c|}{\sqrt{a^2+b^2}}\\\\\sf D_{P,r}=\dfrac{| 3\cdot1+4\cdot3-5|}{\sqrt{3^2+4^2}}\\\\\sf D_{P,r}=\dfrac{10}{\sqrt{25}}\\\\\sf D_{P,r}=\dfrac{10}{5}\\\\\sf D_{P,r}=2\end{array}}$